Several Complex Variables VII

H. Grauert

ISBN 10: 3642081509 / ISBN 13: 9783642081507

Published by Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, DE, 2010

About this Item

Of making many books there is no end; and much study is a weariness of the flesh. Eccl. 12.12. 1. In the beginning Riemann created the surfaces. The periods of integrals of abelian differentials on a compact surface of genus 9 immediately attach a g­ dimensional complex torus to X. If 9 2, the moduli space of X depends on 3g - 3 complex parameters. Thus problems in one complex variable lead, from the very beginning, to studies in several complex variables. Complex tori and moduli spaces are complex manifolds, i.e. Hausdorff spaces with local complex coordinates Z 1, . , Zn; holomorphic functions are, locally, those functions which are holomorphic in these coordinates. th In the second half of the 19 century, classical algebraic geometry was born in Italy. The objects are sets of common zeros of polynomials. Such sets are of finite dimension, but may have singularities forming a closed subset of lower dimension; outside of the singular locus these zero sets are complex manifolds.

Seller Inventory # LU-9783642081507

Bibliographic Details

• Title: Several Complex Variables VII
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, DE
• Publication Date: 2010
• Language: English
• ISBN 10: 3642081509
• ISBN 13: 9783642081507
• Binding: Paperback
• Edition: 1st ed. Softcover of orig. ed. 1994.
• Condition: New

About this title

Synopsis

This volume of the Encyclopaedia offers a systematic introduction and a comprehensive survey of the theory of complex spaces. This is an important subject in the theory of several complex variables. Two of the authors, Grauert and Remmert, are internationally known outstanding experts who have developed substantial parts of the field. The authors have written for graduate students and researchers in complex analysis, algebraic geometry and differential geometry. The book will also be a valuable source of information for mathematical physicists.